Total energy non-conservation for explicit time dependent potentials

Click For Summary
SUMMARY

The discussion centers on the principle that total energy is not conserved when dealing with explicit time-dependent potentials, represented as U(x,t). A participant argues that while the potential energy of a test charge changes due to the movement of a charged particle, the overall energy remains conserved as the energy expended in altering the potential is accounted for. This highlights the distinction between local energy changes and the conservation of total energy in dynamic systems.

PREREQUISITES
  • Understanding of classical mechanics and energy conservation principles
  • Familiarity with potential energy concepts in electrostatics
  • Knowledge of time-dependent potentials in physics
  • Basic grasp of energy transfer in dynamic systems
NEXT STEPS
  • Study the implications of time-dependent potentials in quantum mechanics
  • Explore the mathematical formulation of energy conservation in non-conservative systems
  • Investigate case studies involving explicit time-dependent potentials in electromagnetism
  • Learn about the role of work-energy principles in dynamic systems
USEFUL FOR

Physics students, educators, and researchers interested in energy conservation laws, particularly in the context of time-dependent potentials and their implications in classical and quantum mechanics.

brotherbobby
Messages
756
Reaction score
170
I read from a book that the "total energy is not preserved when the potential depends explicitly on time", i.e. U(x,t). Can anyone show or prove it?

Many thanks.
 
Physics news on Phys.org
Total energy will be conserved. What happens is that you will be spending some energy in changing the potential U.

For instance, consider the potential energy of some test charge, T, placed near some charged particle, A. Of course the potential energy of T will change if you move particle A around. So, in that sense, the test charge's energy is changing. But anything you lose or gain will be covered by the energy used in moving particle A.
 

Similar threads

Graduate Finding the potential energy if force depends on both position and time
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad How does calculus of variations handle explicit time dependence in Lagrangian?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad System, potential energy, and nonconservative forces
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Is Mechanical Energy Conserved for Non-Conservative Forces?
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Conservative forces and internal and external forces
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad How to interpret this definition of potential energy?
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Conservative forces, Nonconservative forces and Potential Energy
  • · Replies 9 ·
Replies
9
Views
4K
Graduate When do time dependent constraints mean energy conservation?
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Energy Conservation and Time-Dependent Potentials
  • · Replies 4 ·
Replies
4
Views
7K
Graduate Effective potential in a central field
  • · Replies 3 ·
Replies
3
Views
2K